The formula to calculate the equation of a line between two points is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us pick any two points for both the two lines and find the equation of the lines.
Line 1
[tex]\begin{gathered} (x_1,y_1)=(-2,0) \\ (x_2,y_2)=(1,3) \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \frac{y-0}{x--2}=\frac{3-0}{1--2} \\ \frac{y}{x+2}=\frac{3}{1+2} \\ \frac{y}{x+2}=\frac{3}{3} \\ \frac{y}{x+2}=1 \\ y=1(x+2) \\ y=x+2 \\ x-y=-2...........1 \end{gathered}[/tex]
Hence, the equation of the line is
[tex]x-y=-2..........1[/tex]
Line 2
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,3) \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \frac{y-0}{x-0}=\frac{3-0}{1-0} \\ \frac{y}{x}=\frac{3}{1} \\ \frac{y}{x}=3 \\ y=3x \\ y-3x=0.............2 \end{gathered}[/tex]
Hence, the equation of the line is,
[tex]y-3x=0...............2[/tex]
Therefore, the system of equations are
[tex]y-3x=0;x-y=-2\text{ \lparen Option 3\rparen}[/tex]
